(in Hz)

RHPzero =

2

L

(in V/s)

n = 1+

2mc

m1

(no unit)

Leff =

L

(D')

2

Z

c

(in rad/s)

2fs

nD'

#

(

)

LM3551, LM3552

www.ti.com

SNVS371D – AUGUST 2005 – REVISED MAY 2013

COMPENSATION

DC Gain and Open-Loop Gain

Since the control stage of the converter forms a complete feedback loop with the power components, it forms a

closed-loop system that must be stabilized to avoid positive feedback and instability. A value for open-loop DC

gain will be required, from which you can calculate, or place, poles and zeros to determine the crossover

frequency and the phase margin. A high phase margin (greater than 45°) is desired for the best stability and

transient response. For the purpose of stabilizing the LM3551/2, choosing a crossover point well below where the

right half plane zero is located will ensure sufficient phase margin.

After this value is known, you can calculate the crossover visually by placing a

−20dB/decade slope at each pole,

and a +20dB/decade slope for each zero. The point at which the gain plot crosses unity gain, or 0dB, is the

crossover frequency. If the crossover frequency is less than ½ the RHP zero, the phase margin should be high

(12)

(13)

(14)

(15)

mc

≊ 0.072 × fs (in V/s)

(16)

(17)

are found in the Electrical Characteristics table.

Right Half Plane Zero

A current mode control boost regulator has an inherent right half plane zero (RHP zero). This zero has the effect

of a zero in the gain plot, causing an imposed +20dB/decade on the rolloff, but has the effect of a pole in the

phase, subtracting another 90° in the phase plot. This can cause undesirable effects if the control loop is

influenced by this zero. To ensure the RHP zero does not cause instability issues, the control loop should be

designed to have a bandwidth of less than ½ the frequency of the RHP zero. This zero occurs at a frequency of:

(18)

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